Contour Error Research Articles

The Shape of the Fused Spine is Associated With Acute Proximal Junctional Kyphosis in Adult Spinal Deformity: An Assessment Based on Vertebral Pelvic Angles.

Retrospective review of prospective database. Vertebral pelvic angles (VPAs) account for complexity in spine shape by assessing the relative position of each vertebra with regard to the pelvis. This study uses VPAs to investigate the shape of the fused spine after T10-pelvis fusion, in patients with adult spinal deformity (ASD), and then explores its association with proximal junctional kyphosis (PJK). Included patients had radiographic evidence of ASD and underwent T10-pelvis realignment. VPAs were used to construct a virtual shape of the post-operative spine. VPA-predicted and actual shapes were then compared between patients with and without PJK. Logistic regression was used to identify components of the VPA-based model that were independent predictors of PJK occurrence and post-operative shape. 287 patients were included. VPA-predicted shape was representative of the true post-operative contour, with a mean point-to-point error of 1.6-2.9% of the T10-S1 spine length. At 6-weeks follow-up, 102 patients (35.5%) developed PJK. Comparison of the true post-operative shapes demonstrated that PJK patients had more posteriorly translated vertebrae from L3 to T7 (P < .001). Logistic regression demonstrated that L3PA (P = .047) and T11PA (P < .001) were the best independent predictors of PJK and were, in conjunction with pelvic incidence, sufficient to reproduce the actual spinal contour (error <3%). VPAs are reliable in reproducing the true, post-operative spine shape in patients undergoing T10-pelvis fusion for ASD. Because VPAs are independent of patient position, L3PA, T11PA, and PI measurements can be used for both pre- and intra-operative planning to ensure optimal alignment.

Adaptive nonsingular terminal sliding mode control of robot manipulator based on contour error compensation

To achieve accurate contour tracking of robotic manipulators with system uncertainties, external disturbance and actuator faults, a cross-coupling contour adaptive nonsingular terminal sliding mode control (CCCANTSMC) is proposed. A nonsingular terminal sliding mode manifold is developed which eliminates the singularity completely. In order to avoid the demand of the prior knowledge of system uncertainties, external disturbance and actuator faults in practical applications, an adaptive tuning approach is proposed. The stability of the proposed control strategy is demonstrated by the finite-time stability theory. Then, the developed controller combines adaptive nonlinear terminal sliding mode control (ANTSMC) of joint trajectory tracking and proportion–differentiation control of end-effector contour tracking by introducing the coupling factor between multiple axes based on Jacobian. Moreover, a unified framework of cross-coupling contour compensation and reference position pre-compensation is built. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control strategy.

Five-Axis Contour Error Control Based on Spatial Iterative Learning

In this paper, a contour error control strategy based on spatial iterative learning control (sILC) is developed for repetitive processing of five-axis computer numerical control (CNC) machine tools. A curve approximation method with an adaptive moving window is developed to achieve accurate tool position and orientation contour error estimation, and a five-axis contour error control strategy based on sILC is proposed. The compensation method is derived using an sILC algorithm to modify the geometric reference path instead of modifying the controller. The experimental results show that the proposed control strategy reduces contour errors of five-axis CNC machine tools, and it outperforms the traditional tracking error control. Note to Practitioners—This paper aims to propose an effective five-axis contour error control scheme. At present, most of the five-axis contour error control methods rely on the modification of the controller, which is not allowed in commercial CNC systems. Therefore, we propose a five-axis contour error compensation algorithm based on sILC, which modifies the system’s reference path. Experimental results show that the proposed method can reduce the five-axis contour errors, while maintaining the machining efficiency.

Intelligent feedrate optimization using a physics-based and data-driven digital twin

Intelligent manufacturing machines envisioned for the future must be able to autonomously select process parameters that maximize their speed while adhering to quality specifications. Accordingly, this paper proposes a framework and methodology for using a physics-based and data-driven digital twin of a feed drive to maximize feedrate while respecting kinematic and contour error limits. To correct for inaccuracies introduced by unmodeled dynamics and disturbances, the data-driven model is updated on-the-fly using sensor feedback. Experiments on a 3-axis CNC machine tool prototype are used to demonstrate up to 35% cycle time reduction without violating error tolerances compared to the status quo.

Inertia matching of CNC cycloidal gear form grinding machine servo system

Reasonable ratio between the load inertia and servo motor inertia plays a decisive role for the dynamic performance and stability of the servo system, as well as the machining accuracy of the whole CNC machine. In order to improve the control performance and contour machining accuracy of the servo system of the CNC cycloidal gear form grinding machine, an optimization design method of the inertia matching for the CNC cycloidal gear form grinding machine servo system is proposed. The two-mass servo driving closed-loop PID control system is constructed, the influence of the different inertia ratios on the dynamic performance and contour errors of the servo system are deeply analyzed, and the inertia ratio is optimized to satisfied with the servo system performance requirements. Finally, the feasibility and practicability of the optimization design method of inertia matching are verified through the inertia ratio optimization grinding experiments of the cycloid gear in the CNC gear form grinding machine. This inertia matching optimization design method provides a valuable reference for the further design of CNC machine servo system.

Iterative learning contouring control: Theory and application to biaxial systems

This paper is concerned with the iterative learning control (ILC) for the contouring control of multi-axis motion system. A novel ILC algorithm, which is called iterative learning contouring control (ILCC), is proposed and verified with biaxial motion systems. In motion control, conventional ILC requires that the number of control objectives is the same as the number of command inputs, which is called square property. This allows for the formulation of transfer function or matrix inversion. The unique feature of contouring control is its non-square property. For contouring control, conventional ILC circumvents the non-square property by adopting the configuration of cross-coupled control (CCC). In other words, the estimated contour error is decomposed into components of individual axis for compensation by ILC and thus the contour error is reduced indirectly. The proposed ILCC can deal with the non-square property and can directly reduce the contour error by adopting the equivalent contour error as the control objective of the ILC. The equivalent contour error represents an accurate contour error model and hence better contouring accuracy can be achieved. The ILCC algorithm is implemented on two platforms, an XY table and a commercial CNC machine tool. Experiments on the contouring control of a circular path with different speeds and a B-spline path are conducted. It is found that the contour error can be reduced about 88% after several learning iterations. The experimental results confirm the effectiveness of the proposed method and show the excellent contouring performance.

Digital Twin Modelling Method of Five-Axis Machine Tool for Predicting Continuous Trajectory Contour Error

The CNC machine tool is the passive executor of machining code. It cannot predict the machining accuracy during machining. If the error is found to be out of tolerance after processing, it will not only scrap the parts, but also greatly affect the processing efficiency. This phenomenon is very prominent when machining sculptured surface parts with five-axis machine tools. Therefore, this paper proposes a Digital Twin (DT) modeling method of five-axis machine tools for predicting Continuous Trajectory Contour Error (CTCE) caused by tracking errors and geometric errors. The DT consists of three parts: the Setpoints Trajectory (ST) model, the Actual Trajectory (AT) model considering tracking errors and geometric errors and the CTCE model. For a specific machine tool, according to the basic geometric information of the machine tool (tool length, kinematic chain information, etc.) and 41 geometric errors, the DT can be established. Inputting the Setpoints Positions (SPs) and the Linear Encoder Detection Positions (LEDPs), the DT can be used to predict the Tool-Tip Position Trajectory (TTPT) contour error and the Tool Orientation Trajectory (TOT) contour error. In order to verify the proposed method experimentally, the KMC400S U five-axis machine tool is selected to establish its DT by which the contour error of the S-shaped trajectory are predicted offline. Then, the DMU50 five-axis machine tool is selected to establish its DT to predict the contour error of the circular trajectory in real time. Combined with the deep motion mechanism, this paper proposes a DT modeling method for the vertical application scene of parts machining accuracy prediction, which is of great significance to developing the DT application theory and ensuring the machining accuracy of parts.

Disturbance-Observer-Based Dual-Position Feedback Controller for Precision Control of an Industrial Robot Arm

Recently, the fourth industrial revolution has accelerated the application of multiple degrees-of-freedom (DOF) robot arms in various applications. However, it is difficult to utilize robot arms for precision motion control because of their low stiffness. External loads applied to robot arms induce deflections in the joints and links, which deteriorates the positioning accuracy. To solve this problem, control methods using a disturbance observer (DOB) with an external sensory system have been developed. However, external sensors are expensive and have low reliability because of noise and reliance on the surrounding environment. A disturbance-observer-based dual-position feedback (DOB-DPF) controller is proposed herein to improve the positioning accuracy by compensating for the deflections in real time using only an internal sensor. The DOB was designed to derive the unpredictable disturbance torque applied to each joint using the command voltage generated by the position controller. The angular deflection of each joint was calculated based on the disturbance torque and joint stiffness, which were identified experimentally. The DPF controller was designed to control the joint motor while simultaneously compensating for angular deflection. A five-DOF robot arm testbed with a position controller was constructed to verify the proposed controller. The contouring performance of the DOB-DPF controller was compared with that of a conventional position controller with an external load applied to the end effector. The increases in the root mean square values of the contour errors were 1.71 and 0.12 mm with a conventional position controller and the proposed DOB-DPF controller, respectively, after a 2.2 kg weight was applied to the end effector. The results show that the contour error caused by the external load is effectively compensated for by the DOB-DPF controller without an external sensor.

A Study of 2D Contour Measurement System at Tool Center Point of Machine Tools

This study proposes a 2D contour measurement system at the tool center point (TCP) that consists of a Blu-ray pickup head and position sensitive detector (PSD). The TCP displacement is equivalent to the relative position between the tool and workpiece. When the machine tools operate the machine part along the desired contour, the TCP displacement affects the machining geometric accuracy. To evaluate the TCP displacement, the contour errors are measured by the cross-grid encoder (KGM) in practice. However, it is difficult to install KGM as it is large and expensive. In this study, an optical measurement system (OMS) is constructed to measure the TCP displacement, named TCP-OMS. A Blu-ray pickup head was installed on the spindle as a tool, and a PSD was installed on the table as a workpiece. To enhance the measurement signal’s resolution and precision of TCP-OMS, the noise was reduced by an AC voltage stabilizer, a DC regulator, and a low-pass filter. The experimental results show that the resolution of displacement measurement was less than 1 μm, and the linearity regions of the X-orientation and Y-orientation were ±3 mm. The motion test on the circular paths were performed on an actual machine tool, and the repeatability tests of this measurement system were verified. The measurement data of circular paths were collected by TCP-OMS and KGM and the results were then compared. When the feed rate of the circular paths increased, the circular deviations were magnified, simultaneously. The axis reversal spikes were observed at the quadrants of a circular path. These measurement results of TCP-OMS matched with the measurement results of KGM. The TCP-OMS developed in this study is characterized by simple installation, compactness, and a low price. It is suitable for 2D contour measurement at the tool center point of machine tools.

Toolpath interpolation with novel corner smoothing technique

• Propose a novel filter-based corner smoothing with double filter technique for CNC machining. • Derive analytical formulations for contour errors with satisfying kinematic constraints. • Design filter order and corner speed to ensure that acceleration, jerk and contour error. • Achieve higher machining efficiency and contour accuracy as compared to the state-of-art technique. In this study, a novel filter-based corner smoothing with double filter (FCSDF) technique is proposed to generate interpolated trajectories for high-speed machine tools. The technique uses a double filter to smooth segment junctions and limit axial jerk. The novelty of this study is to derive an analytical formulation for corner contour error and to find the relationship between corner speed and contour error. The FCSDF algorithm provides a systematic way to design filter order and to determine the corner speed to ensure that acceleration, jerk and contour error are confined. As a result, the technology can achieve both high machining accuracy and efficiency and is easy to implement in real time. Finally, the FCSDF is validated using a multisegment trajectory, and the experimental results verify the effectiveness in improving the contouring performance and cycle time.

Analysis of the Impact of Circular Contour Error Based on CNC Machine

To improve the processing accuracy of the CNC machine, the errors caused by uneven pitch spacing between the servo feeding axes of the NC machine are analyzed. With the combination of the principle of plane circular contour motion track synthesis, the influence of the pitch errors produced by the X and Y axes on the circular contour errors is analyzed. Finally, the experimental platform is adopted to analyze the data before and after screw pitch error compensation with a spherical rod. The results verify that the screw pitch errors impact the outline errors, and the proportion of mismatch errors was reduced by 96.88% after screw pitch errors compensation.

Novel Cross-Coupling Position Command Shaping Controller Using H ∞ in Multiaxis Motion Systems

A new structure of cross-coupling position command shaping controller using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> control scheme for the precise tracking in the multiaxial motion control is proposed in this article, together with its stability analysis.This new structure has the advantage that the controller has a simpler design process and robuster performance than the conventional ones. The proposed controller is evaluated and compared experimentally with an uncoupled controlled and conventional system. The experimental results show that the new structure remarkably reduces contour error. In addition, this new controller can be implemented easily on a majority of motion systems in use today via reprogramming the reference position command subroutine.

Industrial Robot Contouring Control Based on Non-Uniform Rational B-Spline Curve

This paper presents a novel algorithm about the industrial robot contouring control based on the NURBS (non-uniform rational B-spline) curve. First, aiming at the error between the industrial robot’s actual trajectory and the desired trajectory, the contour error is proposed as the trajectory evaluation index, and the estimation algorithm of contour error based on the tangent approximation is proposed. Based on the tangent approximation algorithm, the estimation algorithm of contour error in the local task coordinate frame is proposed to realize the transformation from the Cartesian coordinate frame to the local task coordinate frame. Second, according to the configuration of the industrial robot, a modified cross-coupling control scheme based on the local task coordinate frame is designed. Finally, the Bernoulli’s lemniscate curves are constructed by NURBS curve and five-order polynomial curve, respectively, and they are symmetrical. The contrast experiment is designed using the two types of constructed Bernoulli’s lemniscate curves as the incentive trajectory. Through the analysis and comparison between the obtained uniaxial tracking error and the contour error curve of the two incentive trajectories, it is concluded that the incentive trajectory constructed by the NURBS curve has better contour control performance than that constructed by the five-order polynomial curve. The results drawn from this paper lay a certain foundation for the future high-precision contouring control of industrial robots.

Error estimation and cross-coupled control based on a novel tool pose representation method of a five-axis hybrid machine tool

Five-axis hybrid machine tools combine the advantages of series and parallel mechanisms; however, the time-varying, non-linear, and strong coupled characteristics of parallel mechanisms cause contour control difficulties, particularly during high-speed motion. To solve this problem, this study explores the error-transfer laws between the five feed axes, tool centre position (TCP), and tool orientation (TO). It proposes a new tool-pose representation method, called ‘TP’, for five-axis machine tools; and designs a cross-coupled controller taking TP as the control target. Moreover, a kinematic model of the hybrid machine tool is established, and the error transfer law is solved through the first-order differentiation of the kinematic model. Subsequently, two points are taken on the tool axis, the redundancy of coordinates is removed by coordinate transformation, and TP is achieved. Finally, a cross-coupled controller is designed. The input of the controller are the tracking errors obtained according to the five feed-axes commands and encoder feedbacks. In the controller, according to the laws of error transfer, the TP contour error is estimated in real time, and the control variables are assigned to the feed axes. Finally, taking a five-axis hybrid machine tool as an example, the error transfer characteristic analysis as well as error estimation and cross-coupled control (CCC) experiments are performed. The experimental results obtained through the numerical control (NC) program feedback of the computer numerical control (CNC) system verify the correctness of the theory and validity of the method.

A NURBS Curve Interpolator Based on Double-Step Signal and Finite Impulse Response Filters

Abstract In order to solve the problem that the traditional trajectory planning method cannot flexibly control the velocities and the arrival time of critical points in the trajectory, this paper proposes a non-uniform rational B-spline interpolator based on double-step signal and finite impulse response filters. The interpolator consists of two modules: a pre-processing module and a real-time interpolation module. To reduce the contour error, first, the pre-processing module scans the curve for critical points and sets their velocities according to the chord error. Then, the curve is split, and for each segment, the length and inverse length functions are calculated to eliminate the length error and enhance the real-time performance. Moreover, to control the arrival time and smooth the velocity, the real-time interpolation module generates the trajectory by processing the double-step signal with three finite impulse response filters, which satisfies the constraints of velocity, acceleration, jerk, and displacement. Simulation results indicate that the proposed interpolator can accurately reach the critical points at the set arrival time with smooth velocity and low chord error, and experimental results on a SCARA robot show that the proposed interpolator is feasible and effective.

Research on high-speed and high-precision laser processing algorithm based on macro-micro platform

Aiming at the problem that XY motion platform cannot realize high-speed and high-precision machining simultaneously, a high-speed and high-precision laser processing algorithm is proposed based on the macro-micro structure of laser cutter with a laser galvanometer scanner. The velocity planning of macro platform and composite motion is carried out by applying finite impulse response (FIR) filters three times, and velocity planning of micro platform is obtained by vector subtraction method. The motion decomposition of the macro-micro platform is realized accurately. The macro platform is responsible for large-format movement, and the micro platform is responsible for fast-speed turning. Velocity overlap of adjacent segments is employed to improve the machining efficiency. The constraints are established to determine the overlapping time, so that the algorithm can realize high-speed machining without introducing contour error, and ensure that the velocity, acceleration, and jerk of the macro platform can be processed within the limit range. Experiment and simulation analysis show that compared with using only the XY platform, the total machining time of using the macro-micro platform with the algorithm proposed in this paper is reduced by more than 35%.

Dual-Mode Synchronization Predictive Control of Robotic Manipulator

Abstract To reduce the contour error of the end-effector of a robotic manipulator during trajectory tracking, a dual-mode synchronization predictive control is proposed. First, the dynamic model of n-degree-of-freedom (n-DOF) robotic manipulator is discretized by using the Taylor expansion method, and the mapping relationship between the joint error in joint space and the contour error in task space is constructed. Second, the synchronization error and the tracking error in joint space are defined, and the coupling error of joints is derived through the coupling coefficient λ. Third, a dual-mode synchronization predictive control is proposed, and the stability of the proposed control system is guaranteed using constraint set conditions. Finally, numerical simulation and experimental results are shown to prove the effectiveness of the proposed control strategy.

CNC 공작기계의 고정밀 윤곽가공을 위한 가변 윤곽오차 모델

Studies have been conducted on various contour error models applied to cross-coupling control systems, which are essential for achieving contour accuracies in multi-axis CNC systems. Most of these studies examine contour error models for straight, corner, and curved tool paths. However, there are limitations to applying these existing works in multi-axis tool paths because the straight, corner, and curved tool paths may coexist. Therefore, this paper presents a variable contour error model for cross-coupling control systems to achieve high-precision contour machining. The proposed variable contour error model allows real-time changes to the contour error model based on the tool path curvature. The proposed model was evaluated by implementing a cross-coupling control system on a PC-based three-axis CNC testbed. From the experimental results, the usefulness of the proposed model was confirmed in terms of the contour accuracy.

Contouring Control of a Five-Axis Machine Tool with Equivalent Errors

In this study, the contouring control problem of a five-axis machine tool was examined. Due to the rotation axes, there are two coordinate systems involved in the five-axis machine tool, namely the workpiece coordinate system and machine coordinate system. The five-axis machine tool is required to follow a given desired path with tool orientation specified in the workpiece coordinate system. However, the system dynamics of the machine tool is described in the machine coordinates. Kinematic transformations exist between the two coordinate systems. One challenge of the problem is to design a controller in the machine coordinate system that will meet the requirements in the workpiece coordinate system. Another challenge is to minimize both the position contour error and tool orientation error. The method of equivalent errors is adopted to design the contouring controller. The desired path and tool orientation in the workpiece coordinate system are transformed into a five-dimensional hyper-curve in the machine coordinate system. A contouring controller was designed to follow the five-dimensional hyper-curve using the method of equivalent errors. Both numerical and experimental results validate the effectiveness of the proposed contouring control method.

Research on Processing Error of Special Machine Tool for VH-CATT Cylindrical Gear

The variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear is a new gear suitable for heavy loads and high speed. The special structure of the gear provides excellent mechanical properties but also increases the processing difficulty. The special machine tool for VH-CATT gear provides a prerequisite for mass production, but the machining accuracy remains to be improved. Therefore, this paper proposes a Kriging model based on the glowworm swarm optimization algorithm of scene understanding (SGSO) to study the relationship between input parameters and output precision. Then, the SGSO algorithm is used to optimize the parameters of the Gaussian mutation function in the Kriging model to improve its fitting accuracy. When solving four groups of tooth profile and tooth direction errors, the key precision index, R2, of SGSO-Kriging all exceed 0.95. Additionally, the feasibility of the model is verified by the residual diagram and the box diagram. The contour diagram and error results show that reducing the feeding velocity, vf, can improve accuracy most efficiently, and the increase of rotational speed, n, is more conducive to the accuracy of the tooth surface than the acceleration of the coolant, vQ. The above research provides an optimization strategy of gear machining accuracy and a theoretical basis for the promotion of the VH-CATT gear.